Power-series solution of the L-fractional logistic equation

Abstract

We consider the L-fractional derivative, which has been proposed in the literature to study fractional differentials in geometry and processes in mechanics. Our context is population growth and epidemiology, for which the use of L-derivatives is motivated by transitions. Using power series, we solve the logistic differential equation model under this fractional derivative. Several conclusions on the method, the derivative, and the singularity of the associated kernel are reached. Fractional Euler numbers, related to the logistic map and the famous Riemann zeta function, are also introduced.